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Activating and inhibiting connections in biological network dynamics.

McDonald D, Waterbury L, Knight R, Betterton MD - Biol. Direct (2008)

Bottom Line: However, knowledge of network topology does not allow one to predict network dynamical behavior--for example, whether deleting a protein from a signaling network would maintain the network's dynamical behavior, or induce oscillations or chaos.Reviewed by Sergei Maslov, Eugene Koonin, and Yu (Brandon) Xia (nominated by Mark Gerstein).For the full reviews, please go to the Reviewers' comments section.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Physics, University of Colorado, 390 UCB, Boulder, CO 80309, USA. daniel.mcdonald@colorado.edu

ABSTRACT

Background: Many studies of biochemical networks have analyzed network topology. Such work has suggested that specific types of network wiring may increase network robustness and therefore confer a selective advantage. However, knowledge of network topology does not allow one to predict network dynamical behavior--for example, whether deleting a protein from a signaling network would maintain the network's dynamical behavior, or induce oscillations or chaos.

Results: Here we report that the balance between activating and inhibiting connections is important in determining whether network dynamics reach steady state or oscillate. We use a simple dynamical model of a network of interacting genes or proteins. Using the model, we study random networks, networks selected for robust dynamics, and examples of biological network topologies. The fraction of activating connections influences whether the network dynamics reach steady state or oscillate.

Conclusion: The activating fraction may predispose a network to oscillate or reach steady state, and neutral evolution or selection of this parameter may affect the behavior of biological networks. This principle may unify the dynamics of a wide range of cellular networks.

Reviewers: Reviewed by Sergei Maslov, Eugene Koonin, and Yu (Brandon) Xia (nominated by Mark Gerstein). For the full reviews, please go to the Reviewers' comments section.

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The activating fraction and dynamics of random (Erdös-Renyi) networks. A, C, E, G: Fraction of networks whose dynamics reach steady state, as a function of activating fraction a. B, D, F, H: Average oscillation period of network dynamics, as a function of a. The network size is 10 (A, B), 20 (C, D), 50 (E, F), or 100 (G, H). The number of connections per node is 1 (black circle), 2 (blue square), 5 (red diamond) 8 (green +), or 10 (black triangle). For a near 1, the network dynamics are highly likely to reach steady state, independent of other parameters (A, C, E, G). For a near 0, the steady state fraction is between 7 × 10-4 and 0.25, depending on the network degree. For a near 1, the average period is close 1, which corresponds to steady state (B, D, F, H). For a near 0, the period is close to 2, because the activity of network nodes oscillates between off and on. For a near 0.5, the period has a maximum. The maximum oscillation period increases with the size and degree of the network.
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Figure 2: The activating fraction and dynamics of random (Erdös-Renyi) networks. A, C, E, G: Fraction of networks whose dynamics reach steady state, as a function of activating fraction a. B, D, F, H: Average oscillation period of network dynamics, as a function of a. The network size is 10 (A, B), 20 (C, D), 50 (E, F), or 100 (G, H). The number of connections per node is 1 (black circle), 2 (blue square), 5 (red diamond) 8 (green +), or 10 (black triangle). For a near 1, the network dynamics are highly likely to reach steady state, independent of other parameters (A, C, E, G). For a near 0, the steady state fraction is between 7 × 10-4 and 0.25, depending on the network degree. For a near 1, the average period is close 1, which corresponds to steady state (B, D, F, H). For a near 0, the period is close to 2, because the activity of network nodes oscillates between off and on. For a near 0.5, the period has a maximum. The maximum oscillation period increases with the size and degree of the network.

Mentions: For a wide range of conditions, the activating fraction a is strongly correlated with the probability that the dynamics of a random network reach steady state. For a near 1, nearly all runs of the network dynamics reach steady state, while for a near 0, few runs reach steady state; the network dynamics typically oscillate (fig. 2). When a = 0, ~0.01% to 10% of runs reach steady state, depending on network degree. The probability of reaching steady state is only weakly dependent on the size of the network, if the number of connections per node is fixed (fig. 2). Altering the typical magnitude of connection strengths has little effect on the dynamics, because the dynamics are highly saturated (see Methods).


Activating and inhibiting connections in biological network dynamics.

McDonald D, Waterbury L, Knight R, Betterton MD - Biol. Direct (2008)

The activating fraction and dynamics of random (Erdös-Renyi) networks. A, C, E, G: Fraction of networks whose dynamics reach steady state, as a function of activating fraction a. B, D, F, H: Average oscillation period of network dynamics, as a function of a. The network size is 10 (A, B), 20 (C, D), 50 (E, F), or 100 (G, H). The number of connections per node is 1 (black circle), 2 (blue square), 5 (red diamond) 8 (green +), or 10 (black triangle). For a near 1, the network dynamics are highly likely to reach steady state, independent of other parameters (A, C, E, G). For a near 0, the steady state fraction is between 7 × 10-4 and 0.25, depending on the network degree. For a near 1, the average period is close 1, which corresponds to steady state (B, D, F, H). For a near 0, the period is close to 2, because the activity of network nodes oscillates between off and on. For a near 0.5, the period has a maximum. The maximum oscillation period increases with the size and degree of the network.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2651858&req=5

Figure 2: The activating fraction and dynamics of random (Erdös-Renyi) networks. A, C, E, G: Fraction of networks whose dynamics reach steady state, as a function of activating fraction a. B, D, F, H: Average oscillation period of network dynamics, as a function of a. The network size is 10 (A, B), 20 (C, D), 50 (E, F), or 100 (G, H). The number of connections per node is 1 (black circle), 2 (blue square), 5 (red diamond) 8 (green +), or 10 (black triangle). For a near 1, the network dynamics are highly likely to reach steady state, independent of other parameters (A, C, E, G). For a near 0, the steady state fraction is between 7 × 10-4 and 0.25, depending on the network degree. For a near 1, the average period is close 1, which corresponds to steady state (B, D, F, H). For a near 0, the period is close to 2, because the activity of network nodes oscillates between off and on. For a near 0.5, the period has a maximum. The maximum oscillation period increases with the size and degree of the network.
Mentions: For a wide range of conditions, the activating fraction a is strongly correlated with the probability that the dynamics of a random network reach steady state. For a near 1, nearly all runs of the network dynamics reach steady state, while for a near 0, few runs reach steady state; the network dynamics typically oscillate (fig. 2). When a = 0, ~0.01% to 10% of runs reach steady state, depending on network degree. The probability of reaching steady state is only weakly dependent on the size of the network, if the number of connections per node is fixed (fig. 2). Altering the typical magnitude of connection strengths has little effect on the dynamics, because the dynamics are highly saturated (see Methods).

Bottom Line: However, knowledge of network topology does not allow one to predict network dynamical behavior--for example, whether deleting a protein from a signaling network would maintain the network's dynamical behavior, or induce oscillations or chaos.Reviewed by Sergei Maslov, Eugene Koonin, and Yu (Brandon) Xia (nominated by Mark Gerstein).For the full reviews, please go to the Reviewers' comments section.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Physics, University of Colorado, 390 UCB, Boulder, CO 80309, USA. daniel.mcdonald@colorado.edu

ABSTRACT

Background: Many studies of biochemical networks have analyzed network topology. Such work has suggested that specific types of network wiring may increase network robustness and therefore confer a selective advantage. However, knowledge of network topology does not allow one to predict network dynamical behavior--for example, whether deleting a protein from a signaling network would maintain the network's dynamical behavior, or induce oscillations or chaos.

Results: Here we report that the balance between activating and inhibiting connections is important in determining whether network dynamics reach steady state or oscillate. We use a simple dynamical model of a network of interacting genes or proteins. Using the model, we study random networks, networks selected for robust dynamics, and examples of biological network topologies. The fraction of activating connections influences whether the network dynamics reach steady state or oscillate.

Conclusion: The activating fraction may predispose a network to oscillate or reach steady state, and neutral evolution or selection of this parameter may affect the behavior of biological networks. This principle may unify the dynamics of a wide range of cellular networks.

Reviewers: Reviewed by Sergei Maslov, Eugene Koonin, and Yu (Brandon) Xia (nominated by Mark Gerstein). For the full reviews, please go to the Reviewers' comments section.

Show MeSH